Question

A concrete beam of rectangular cross-section of size 120 mm (width) and 200 mm (depth) is pre-stressed by a straight tendon to an effective force of 150 kN at an eccentricity of 20 mm (below the centroidal axis in the depth direction). The stresses at the top and bottom fibres of the section are

• A. 2.5 N/mm${}^2$(compression), 10N/mm${}^2$ (compression)
• B. 10 N/mm${}^2$(tension), 2.5N/mm${}^2$(compression)
• C. 3.75N/mm${}^2$(tension), 3.75 N/mm${}^2$ (compression)
• D. 2.75 N/mm${}^2$(compression), 3.75 N/mm${}^2$(compression)

Answer 1

The correct option is A 2.5 N/mm${}^2$(compression), 10N/mm${}^2$ (compression)




Prestressing force, P = 150 kN
Eccentricity, e = 20mm
Moment of inertia,

$I=\frac{b{d}^3}{12}=\frac{120\times {200}^3}{12}$

$=80\times {10}^{6}m{m}^4$

Stress at top fibre

$=\frac{P}{A}-\frac{My}{I}$

$=\frac{P}{A}-\frac{(P.e)y}{I}$

$=\frac{150\times {10}^3}{120\times 200}-\frac{(150\times {10}^3\times 20).100}{80\times {10}^6}$

= 6.25 - 3.75

$=2.5N/m{m}^2\left(Compression\right)$

Stress at bottom fibre

$=\frac{P}{A}+\frac{My}{I}=6.25+3.75$

$=10N/m{m}^2$